Animation nodes, instances orientation in a Dodecahedron
This method works for any object which has symmetric faces of the same size. The main idea is to align the instance object's (in your case the Tritube) any axis (local) along the edges of the base object (in your case is the Pentaface).

Note: This method required that any symmetric face of the base object should not have any cutting edge. For example, a cube object should not have a diagonal edge in any its face or in case of Pentaface object:


Step-1: A edge has a start, end, and center. So, the equation below gives the guide for start and end:

Start-Center = guide at the start
End-Center = guide at the end


To solve this for all edges, I have made a Guides for Direction Loop loop-node which takes the vertex locations, edges of the object and two empty vector lists, calculate the guides for each vertex. To simplify further, I have also made a AN-Guides for Direction group-node which automatically creates two empty lists for the Guides for Direction Loop node, so you only need to supply the vertex locations and edges:


Step-2: Then connect the vertex normals to direction and guides from the AN-Guides for Direction group-node to guides of the Direction to Rotation node:

Sometimes, you may need to rotate the instance object (in your case the Tritube) in edit mode to match the direction of the edges of the base object.

Step-3: Here is an example for cube object but same node-tree:


Step-4: I have converted the node-tree of How to call vertex groups in Animation nodes into a group-node for easy usage:


Step-5: Now, you can easily change the z-direction of instances with vertex weight but keeping them align with the edges of the base object with this node-tree:


Complete Node-Tree:


Blend File: